Basic properties
Modulus: | \(4003\) | |
Conductor: | \(4003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(87\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4003.j
\(\chi_{4003}(10,\cdot)\) \(\chi_{4003}(100,\cdot)\) \(\chi_{4003}(117,\cdot)\) \(\chi_{4003}(127,\cdot)\) \(\chi_{4003}(208,\cdot)\) \(\chi_{4003}(214,\cdot)\) \(\chi_{4003}(285,\cdot)\) \(\chi_{4003}(292,\cdot)\) \(\chi_{4003}(316,\cdot)\) \(\chi_{4003}(318,\cdot)\) \(\chi_{4003}(356,\cdot)\) \(\chi_{4003}(412,\cdot)\) \(\chi_{4003}(479,\cdot)\) \(\chi_{4003}(506,\cdot)\) \(\chi_{4003}(785,\cdot)\) \(\chi_{4003}(787,\cdot)\) \(\chi_{4003}(788,\cdot)\) \(\chi_{4003}(913,\cdot)\) \(\chi_{4003}(945,\cdot)\) \(\chi_{4003}(1020,\cdot)\) \(\chi_{4003}(1049,\cdot)\) \(\chi_{4003}(1057,\cdot)\) \(\chi_{4003}(1165,\cdot)\) \(\chi_{4003}(1201,\cdot)\) \(\chi_{4003}(1270,\cdot)\) \(\chi_{4003}(1321,\cdot)\) \(\chi_{4003}(1385,\cdot)\) \(\chi_{4003}(1444,\cdot)\) \(\chi_{4003}(1618,\cdot)\) \(\chi_{4003}(1622,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{87})$ |
Fixed field: | Number field defined by a degree 87 polynomial |
Values on generators
\(2\) → \(e\left(\frac{4}{87}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4003 }(208, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{87}\right)\) | \(e\left(\frac{11}{87}\right)\) | \(e\left(\frac{8}{87}\right)\) | \(e\left(\frac{55}{87}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{10}{87}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{22}{87}\right)\) | \(e\left(\frac{59}{87}\right)\) | \(e\left(\frac{15}{29}\right)\) |